Problem:
A bus starts with 9 people, two of whom are Jack and Mike, and stops at 14 locations. Assuming nobody else gets on the bus, how many ways are there...
a) for people to get off the bus?
b) for people to get off the bus if no 2 people get off at the same stop?
c) for people to get off the bus if Jack and Mike get off together?
-----
My thinking for a) was that since there are 9 people, there are 10 possibilities at each stop (1-9 people get off or no one gets off) and this happens 14 times, so I got 10^14 via the counting principle. I'm not sure if that makes sense, though...
For b) I figured you were removing one possibility each time, so 9^14, and same for c).
Hey Plato, thanks for replying - I think I was saying what you were, but I have never seen the idea of "how many functions from a set" as you were saying, so I don't really know what you mean . Shouldn't you do 10->14 though, as an option is that the people do not give off the bus adds one possibility to the equation? Or am I overthinking?
What Plato is talking about is that there is a function which takes as input a person riding the bus and produces the output of which stop that person gets off at. The number of these functions that exist is the number of ways people can get off the bus. You can assign numbers 1-9 to the people riding the bus and numbers 1-14 to the bus stops. One possible function map is:
(1, 13)
(2, 12)
(3, 2)
(4, 2)
(5, 8)
(6, 8)
(7, 14)
(8, 1)
(9, 3)